This invention relates to digital compensation of a non-linear circuit, and in particular, to linearization of a non-linear power amplifier and transmitter chain.
A concept of applying a digital compensation to restore the quality of an original signal passed through a circuit is a routine. A power amplifier in a radio of a wireless base station or handset is compensated digitally in the baseband to minimize the spectral leakage into adjacent channels. An audio amplifier in a speaker is compensated digitally to achieve high fidelity. In many such examples, variants of Volterra series have been adopted to account for dynamical nature of nonlinearity. Wiener, Wiener-Hammerstein, General Memoryless Polynomial are popular structures for digital pre-distorters, which are used to modify an input signal prior to passing through a non-linear circuit. In general, these structures have an exponential complexity if the polynomial order exceeds 3 to 5, as well as robustness issues due to sensitivity of compensator parameters to variations of a particular device (Device Under Test, DUT), including process, temperature, supply voltage, and other operating conditions.
Referring to FIG. 1, in an example of a linearization of a radio power amplifier, a digital input signal x[n] at a baseband or intermediate frequency is passed through a Digital Pre-Distorter (DPD) 110 to produce a “pre-distorted” input y[n], which is passed through a transmit chain 140 to produce a driving signal p(t) that drives an antenna 150. The transmit chain may include a Digital-to-Analog Converter (DAC) 142, an analog lowpass filter (LPF) 144, and a modulator (e.g., multiplication by a local oscillator) of the output of the LPF 144. The output of the modulator is passed to a power amplifier (PA) 148. The PA 148, as well as other elements in the transmit chain, may introduce non-linearities, which may be manifested in the driving signal p(t) as harmonic and/or intermodulation distortion of the input signal x[n]. To overcome these nolinearities, the DPD 110 also introduces non-linearities that are intended to “pre-invert” (i.e. pre-distort) the non-linear effects of the transmit chain. In some examples, the DPD performs the transformation of the desired signal x[n] to the input y[n] of the transmit chain by using delay elements 120 to form a set of delayed versions of the desired signal, and then using a non-linear polynomial function 130 of those delayed inputs. In some examples, the non-linear function is a Volterra series:y[n]=h0+ΣpΣτ1, . . . ,τphp(τ1, . . . τp)Πj=1 . . . px[n−τj]In some examples, the non-linear function is reduced set of Volterra terms, for example a delay polynomial:y[n]=h0+ΣpΣτhp(τ)x[n−τ]|x[n−τ|(p-1) 
In order to invert the non-linear effects of the transmit chain, in general, a relatively large number of terms of such a series representation are needed, and the coefficients of those terms (e.g., the hp terms) must be accurately set. In general, the coefficients in such approaches are continually updated to maintain good linearization. Various approaches to such continual updating are used, for example, based on incremental updates using y[n] and observation of p(t) (e.g., after demodulation).